In order to measure sensor signals which are based on a variable quantity, it is known to modulate the signals by means of an amplitude modulation. It is furthermore known to carry out the implementation of an amplitude modulation in simple sensors with a restricted computing capacity in digital or discrete form. One demodulation algorithm known for this is, for example, the Goertzel algorithm, see The American Mathematical Monthly, Vol. 65, No. 1 (January, 1958), pp. 34-35, “An Algorithm for the Evaluation of Finite Trigonometric Series”. The designation Goertzel filter can also be found in the prior art. Both terms relate to the same process. The term filter applies more to the implementation as a block of signal processing, while algorithm refers primarily to the sequence of computing operations taking place in such a block. The implementation may optionally be carried out by means of hardware or software.
The Goertzel algorithm determines a complex coefficient, valid for a selected carrier frequency, of a discrete Fourier transform (DFT), and is therefore often referred to as “DFT for a frequency”. The reason for its use is the lower computing outlay compared with DFT when the number of coefficients to be calculated is small. For the measurement of sensor signals according to the type described above, the calculation of a single coefficient is sufficient. The Goertzel algorithm is for this purpose therefore numerically more efficient than the DFT. There are variants of the algorithm, which instead of the complex coefficient determine magnitude and phase or even only one of the two components. These variants differ only in details, and are selected according to the application, i.e. the purpose of the measurement. Both in respect of the prior art and in respect of the invention, the variants may be regarded as one algorithm in terms of all essential features.
Amplitude modulation and the Goertzel algorithm have the disadvantage that they are susceptible to certain perturbation frequencies interfering with the signal frequency or modulation frequency. If, in the frequency band used for the amplitude modulation, there is a strong narrowband perturbation, the frequency and phase of which are unknown, the measurement error caused by this may exceed any limits. An expedient maximum tolerance of the measurement system cannot be specified. The use of amplitude modulation, or the maximum permissible amplitude of perturbations, are limited by this property. Particularly in the application field of safety-relevant automobile components, for example brake systems or steering systems, such failure probability of the sensor signals is unacceptable even if these failures occur only with low probability.
The object of the invention is therefore to provide a method, a signal processing unit or a sensor arrangement, which make it possible with a computing outlay that is as low as possible to implement modulation which is substantially less susceptible to external perturbation frequencies.